A problem of image denoising, when images are corrupted by a non-stationary noise, is considered in this paper. Since, in practice, no a priori information on noise is available, noise statistics should be pre-estimated prior to image denoising. In this paper, deep convolutional neural network (CNN) based method for estimation of a map of local, patch-wise, standard deviations of noise (so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sigma-map</i> ) is proposed. It achieves the state-of-the-art performance in accuracy of estimation of sigma-map for the case of non-stationary noise, as well as estimation of a noise variance for the case of an additive white Gaussian noise. Extensive experiments on image denoising using estimated sigma-maps demonstrate that our method outperforms recent CNN-based blind image denoising methods by up to 6 dB in PSNR, as well as other state-of-the-art methods based on sigma-map estimation by up to 0.5 dB, providing, at the same time, better usage flexibility. A comparison with the ideal case, when denoising is applied using ground-truth sigma-map, shows that a difference of corresponding PSNR values for the most of noise levels is within 0.1-0.2 dB, and does not exceed 0.6 dB.